Mapping the complexity of ecological models

We propose to define the complexity of an ecological model as the statistical complexity of the output it produces. This allows for a direct comparison between data and model complexity. Working with univariate time series, we show that this measure ‘blindly’ discriminates among the different dynamical behaviours a model can exhibit. We then search a model parameter space in order to segment it into areas of different dynamical behaviour and calculate the maximum complexity a model can generate. Given a time series, and the problem of choosing among a number of ecological models to study it, we suggest that models whose maximum complexity is lower than the time series complexity should be disregarded because they are unable to reconstruct some of the structures contained in the data. Similar reasoning could be used to disregard models’ subdomains as well as areas of unnecessary high complexity. We suggest that model complexity so defined better captures the difficulty faced by a user in managing and understanding the behaviour of an ecological model than measures based on a model ‘size’.